Universal inverted flexure
Flexure block fabricated from single piece of material minimizes effect of temperature changes and prevents overstressing of the flexing element.
Hadland, W. O.↗
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Analytical and experimental investigations of human spine flexure.
The authors report on experiments to measure the resistance of fresh human spines to flexion in the upper lumbar and lower thoracic regions and evaluate results by using a combination of strength of materials theory and effects of shear and comparing with data reported by other authors. The test results indicate that the thoraco-lumbar spine behaves approximately as a linear elastic beam, without relaxation effects. The authors formulate a simple continuum dynamic model of the spine simulating aircraft ejection and solve the resulting boundary value problem to illustrate the importance of the flexural mode. A constant cross-section, the selected model is a sinusoidally curved elastic beam with an end mass subjected to a Heaviside axial acceleration at the other end. The paper presents transient response results for the spinal model axial and bending displacements and axial force.-
Moffatt, C. A.↗
Dynamic errors in a tuned flexure-mounted strapdown gyro
Motion induced errors in a tuned, flexure-mounted strapdown gyro are investigated. Analytic expressions are developed for errors induced by linear vibrations, angular motion, and detuning. Sensor-level errors (gyro drift rate) and system-level errors (navigation errors) that are stimulated by an actual dynamic motion environment are computed.
Bortz, J. E., Sr.↗
Large amplitude flexural vibration of thin elastic flat plates and shells
The general equations governing the large amplitude flexural vibration of any thin elastic shell using curvilinear orthogonal coordinates are derived and consist of two coupled, nonlinear, partial differential equations in the normal displacement w and the stress function F. From these equations, the governing equations for the case of shells of revolution or flat plates can be readily obtained as special cases. The material of the shell or plate is isotropic and homogeneous and Hooke's law for the two-dimensional case is valid. It is suggested that the difference between the hardening type of nonlinearity in the case of flat plates and straight beams and the softening type of nonlinearity in the case of shells and rings can, in general, be traced to the amount of curvature present in the underformed median surface of the structure concerned.
Pandalia, K. A. V.↗
Martian lithospheric thickness from elastic flexure theory
The thickness of the elastic lithosphere in the Tharsis region of Mars is estimated from effects due to the surface load of Olympus Mons. Deformation (vertical displacement) and stress are calculated using elastic flexure theory for a range of possible lithospheric thicknesses (T), modeling the lithosphere as a thin elastic shell and the interior as a Newtonian fluid. For T below 150 km, displacement and stress rise rapidly with decreasing thickness. For T near 100 km, deformation of the region surrounding the volcano would be clearly visible in the topography, and resulting tensional stresses exceeding 5 kbar should produce observable fracturing at the surface. In contrast, for T near 200 km deformation is minimal and the tensional stress, being less than a kilobar, would not result in extensive fracturing. Since significant deformation and fracturing are not observed, it is concluded that the Martian elastic lithosphere is at least 150 km in thickness. Seismic, tectonic, and gravity observations all suggest a thick Martian lithosphere as well.
Thurber, C. H.↗
Effect of geometric nonlinearity on the free flexural vibrations of moderately thick rectangular plates
The effect of geometric nonlinearity on the free flexural vibrations of moderately thick rectangular plates is studied in this paper. Finite element formulation is employed to obtain the non-linear to linear period ratios for some rectangular plates. A conforming finite element of rectangular shape wherein the effects of shear deformation and rotatory inertia are included, is developed and used for the analysis. Results are presented for both simply supported and clamped boundary conditions.
Raju, K. K.↗
Testing panels in tension and flexure
Simple jig adapts tensile test machine for simulataneous application of tension and flexure, for evaluating panel composition, processing, and design. Environmental test chamber can be added so that panel properties can be measured at extreme temperatures.
Jing, G. K.↗
Tensile and flexural strength of non-graphitic superhybrid composites: Predictions and comparisons
Equations are presented and described which can be used to predict bounds on the tensile and flexural strengths of nongraphitic superhybrid (NGSH) composites. These equations are derived by taking into account the measured stress-strain behavior, the lamination residual stresses and the sequence of events leading to fracture. The required input for using these equations includes constituents, properties (elastic and strength), NGSH elastic properties, cure temperature, and ply stress influence coefficients. Results predicted by these equations are in reasonably good agreement with measured data for strength and for the apparent knees in the nonlinear stress-strain curve. The lower bound values are conservative compared to measured data. These equations are relatively simple and are suitable for use in the preliminary design and initial sizing of structural components made from NGSH composites.
Chamis, C. C.↗
Tensile and flexural strength of nongraphitic superhybrid composites - Predictions and comparisons
Equations are presented and described which can be used to predict bounds on the tensile and flexural strengths of nongraphitic superhybrid (NGSH) composites. These equations are derived by taking into account the measured stress-strain behavior, the lamination residual stresses and the sequence of events leading to fracture. The required input for using these equations includes constituent composites, elastic and strength properties, NGSH elastic properties, cure temperature, and ply stress influence coefficients. Results predicted by these equations are in reasonably good agreement with measured data for strength and for the apparent 'knees' in the nonlinear stress-strain curve. The lower bound values are conservative compared to measured data. These equations are relatively simple and should be suitable for use in the preliminary design and initial sizing of structural components made from NGSH composites.
Chamis, C. C.↗
Unidirectional Flexural Pivot
Flexural pivot deflects in only one angular direction (either clockwise or counterclockwise) and has a longer operating life than many previous designs. Pivot consists of two rings interconnected by three flat metal parallelograms welded into grooves or slots in inside diameters of rings. Springs flex to relieve compressive stress imparted by angular rotation.
Bahiman, H.↗
Thick plate flexure
Analytical expressions are derived for the displacements and stresses due to loading of a floating, uniform, elastic plate of arbitrary thickness by a plane or axisymmetric harmonic load. The solution is exact except for assumptions of small strains and linear boundary conditions, and gravitation within the plate is neglected. For typical earth parameters its predictions are comparable to those of the usual thin plate theory frequently assumed in studies of lithospheric flexure, gravity and regional isostasy. Even for a very thick lithosphere, which may exist in some regions of Mars, the thin plate theory is a better approximation to the thick plate solution than the elastic half-space limit, except for short-wavelength loads.
Comer, R. P.↗
Propagation of flexural and membrane waves with fluid loaded NASTRAN plate and shell elements
Modeling of flexural and membrane type waves existing in various submerged (or in vacuo) plate and/or shell finite element models that are excited with steady state type harmonic loadings proportioned to e(i omega t) is discussed. Only thin walled plates and shells are treated wherein rotary inertia and shear correction factors are not included. More specifically, the issue of determining the shell or plate mesh size needed to represent the spatial distribution of the plate or shell response is of prime importance towards successfully representing the solution to the problem at hand. To this end, a procedure is presented for establishing guide lines for determining the mesh size based on a simple test model that can be used for a variety of plate and shell configurations such as, cylindrical shells with water loading, cylindrical shells in vacuo, plates with water loading, and plates in vacuo. The procedure for doing these four cases is given, with specific numerical examples present only for the cylindrical shell case.
Kalinowski, A. J.↗
SEASAT observations of lithospheric flexure
Models of lithospheric flexure were tested on SEASAT altimetric observations of the geoid over Outer Rises. These altimeter data were found to provide significant new information about the strength of the oceanic lithosphere. Among the significant results derived from altimeter data is confirmation of the proposition that the effective elastic thickness, T sub e, of the lithosphere increases with age in approximate accord with the relation T sub E approximately equals C times one half the age. SEASAT altimeter data over Outer Rises provide an important constraint on mechanical models of the oceanic lithosphere. These data are quite consistent with an experimentally predicted mechanical model of the lithosphere which indicates that this model may be useful in other geodynamic investigations.
Mcadoo, D. C.↗
Finite element analysis of end notch flexure specimen
A finite element analysis of the end notch flexure specimen for mode II interlaminar fracture toughness measurement was conducted. The effect of friction between the crack faces and large deflection on the evaluation of G sub IIc from this specimen were investigated. Results of this study are presented in this paper.
Mall, S.↗
Finite-element analysis of end-notch flexure specimens
A finite-element analysis of the end-notch flexure specimen for Mode II interlaminar fracture toughness measurement was conducted. The effects of friction between the crack faces and large deflection on the evaluation of G(IIc) from this specimen were investigated. Results of this study are presented in this paper.
Mall, S.↗
A mechanism for precise linear and angular adjustment utilizing flexures
The design and development of a mechanism for precise linear and angular adjustment is described. This work was in support of the development of a mechanical extensometer for biaxial strain measurement. A compact mechanism was required which would allow angular adjustments about perpendicular axes with better than 0.001 degree resolution. The approach adopted was first to develop a means of precise linear adjustment. To this end, a mechanism based on the toggle principle was built with inexpensive and easily manufactured parts. A detailed evaluation showed that the resolution of the mechanism was better than 1 micron and that adjustments made by using the device were repeatable. In the second stage of this work, the linear adjustment mechanisms were used in conjunction with a simple arrangement of flexural pivots and attachment blocks to provide the required angular adjustments. Attempts to use the mechanism in conjunction with the biaxial extensometer under development proved unsuccessful. Any form of in stitu adjustment was found to cause erratic changes in instrument output. These changes were due to problems with the suspension system. However, the subject mechanism performed well in its own right and appeared to have potential for use in other applications.
Ellis, J. R.↗
An Investigation of Energy Transmission Due to Flexural Wave Propagation in Lightweight, Built-Up Structures
A technique to measure flexural structure-borne noise intensity is investigated. Two accelerometers serve as transducers in this cross-spectral technique. The structure-borne sound power is obtained by two different techniques and compared. In the first method, a contour integral of intensity is performed from the values provided by the two-accelerometer intensity technique. In the second method, input power is calculated directly from the output of force and acceleration transducers. A plate and two beams were the subjects of the sound power comparisons. Excitation for the structures was either band-limited white noise or a deterministic signal similar to a swept sine. The two-accelerometer method was found to be sharply limited by near field and transducer spacing limitations. In addition, for the lightweight structures investigated, it was found that the probe inertia can have a significant influence on the power input to the structure. In addition to the experimental investigation of structure-borne sound energy, an extensive study of the point harmonically forced, point-damped beam boundary value problem was performed to gain insight into measurements of this nature. The intensity formulations were also incorporated into the finite element method. Intensity mappings were obtained analytically via finite element modeling of simple structures.
Mickol, John Douglas↗
Finite element analysis of the end notched flexure specimen for measuring Mode II fracture toughness
The paper presents a finite element analysis of the end-notched flexure (ENF) test specimen for Mode II interlaminar fracture testing of composite materials. Virtual crack closure and compliance techniques employed to calculate strain energy release rates from linear elastic two-dimensional analysis indicate that the ENF specimen is a pure Mode II fracture test within the constraints of small deflection theory. Furthermore, the ENF fracture specimen is shown to be relatively insensitive to process-induced cracks, offset from the laminate midplane. Frictional effects are investigated by including the contact problem in the finite element model. A parametric study investigating the influence of delamination length, span, thickness, and material properties assessed the accuracy of beam theory expressions for compliance and strain energy release rate, GII. Finite element results indicate that data reduction schemes based upon beam theory underestimate GII by approximately 20-40 percent for typical unidirectional graphite fiber composite test specimen geometries. Consequently, an improved data reduction scheme is proposed.
Gillespie, J. W., Jr.↗